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# Comparing Numerical Data across Groups

Some of the more interesting investigations can be considered by examining numerical data across groups. The methods required here aren’t really new: all that’s required is to make a numerical plot for each group in the same graph. Here two convenient methods are introduced: side-by-side box plots and hollow histograms.

We will take a look again at the county data set and compare the median household income for counties that gained population from 2010 to 2017 versus counties that had no gain. While we might like to make a causal connection here, remember that these are observational data and so such an interpretation would be, at best, half-baked.

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There were 1,454 counties where the population increased from 2010 to 2017, and there were 1,672 counties with no gain (all but one were a loss). A random sample of 100 counties from the first group and 50 from the second group to give a better sense of some of the raw median income data.

Median Income for 150 Counties, in \$1000s

Population Gain No Population Gain 38.2 43.6 42.2 61.5 51.1 45.7 48.3 60.3 50.7 44.6 51.8 40.7 48.1 56.4 41.9 39.3 40.4 40.3 40.6 63.3 52.1 60.3 49.8 51.7 57 47.2 45.9 51.1 34.1 45.5 52.8 49.1 51 42.3 41.5 46.1 80.8 46.3 82.2 43.6 39.7 49.4 44.9 51.7 46.4 75.2 40.6 46.3 62.4 44.1 51.3 29.1 51.8 50.5 51.9 34.7 54 42.9 52.2 45.1 27 30.9 34.9 61 51.4 56.5 62 46 46.4 40.7 51.8 61.1

53.8 57.6 69.2 48.4 40.5 48.6 43.4 34.7 45.7 53.1 54.6 55 46.4 39.9 56.7 33.1 21 37 63 49.1 57.2 44.1 50 38.9 52 31.9 45.7

46.6 46.5 38.9 50.9 56 34.6 56.3 38.7 45.7 74.2 63 49.6 53.7 77.5 60 56.2 43 21.7 63.2 47.6 55.9 39.1 57.8 42.6 44.5 34.5 48.9 50.4 49 45.6 39 38.8 37.1 50.9 42.1 43.2 57.2 44.7 71.7 35.3 100.2 35.4 41.3 33.6 42.6 55.5 38.6 52.7 63 43.4 56.5

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